You're coming off worse in this argument because you seem to realize on some level they're just using different (possibly wrong) terms in their accurate description of the mechanisms, but then you keep making snide remarks that imply they don't understand the mechanisms.
I think your analogy to flat earth was better. Because sure, treating the earth as flat isn't correct, but it's often a perfectly good approximation, and arguing about whether a big field is flat or not is a giant waste of time. Don't completely dismiss someone because they use those terms.
"Leader" or not, it's basically equivalent. And the process of letting miners input yes/no values for whether they support a proposal into their block, averaged over thousands of blocks, gives you the same result as "voting". So talk about whether those results are useful.
All miners “vote” by hashing and one of them wins. They don’t win because somebody voted for them, they win because they happened to find a satisfactory hash. The chance to win that hash faster than other miners is proportional to hashrate. The hash is determined by the block of transactions entirely, so once you win the race, you don’t get to propose anything other than that one predetermined block.
Which transactions go into a block is decided before any mining for that transaction happens.
Just read, please.